Optical transmission system and multi-core optical fiber

ABSTRACT

An optical transmission system includes an optical transmitting unit that outputs at least one optical signal having a wavelength included in an operation wavelength band and a holey fiber that is connected to the optical transmitting unit. The holey fiber includes a core and a cladding formed around the core. The cladding includes a plurality of holes formed around the core in a triangular lattice shape. The holey fiber transmits the optical signal in a single mode. A bending loss of the holey fiber is equal to or less than 5 dB/m at a wavelength within the operation wavelength band when the holey fiber is wound at a diameter of 20 millimeters.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present continuation application claims the benefit of priorityunder 35 U.S.C. §120 to application Ser. No. 12/545,236, filed on Aug.21, 2009, which is a continuation of international applicationPCT/JP2009/050374 filed on Jan. 14, 2009, and claims the benefit ofpriority under 35 U.S.C. §119 from Japanese Patent Application No.2008-104693 filed on Apr. 14, 2008 and Japanese patent Application No.2008-045980, filed on Feb. 27, 2008. The contents of application Ser.No. 12/545,236 and PCT/JP2009/050374 are incorporated herein byreference in their entireties.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an optical transmission system and amulti-core optical fiber that can be used in the optical transmissionsystem.

2. Description of the Related Art

In optical communications, the transmission capacity has increasedrapidly with developments of an optical amplifier, a signalmodulation/demodulation scheme, and the like. In addition, a demand fordata has been also increasing for sure along with a spread of the fiberto the home (FTTH). Therefore, a further increase of the transmissioncapacity is indispensable. A method of increasing a transmissioncapacity is disclosed in which a holey fiber (hereinafter, referred toas “HF” as appropriate), which is a new type of optical fiber, is usedas an optical transmission line. The holey fiber has a hole structure,and confines a light in the core region by holes. For example, in K.Ieda, K. Kurokawa, K. Tajima, and K. Nakajima, “Visible to infraredhigh-speed WDM transmission over PCF”, IEICE Electron. Express, vol. 4,no. 12, pp. 375-379 (2007), an optical transmission line with a lengthof 1 kilometer is deployed using a photonic-crystal fiber (PCF), whichis a kind of the holey fiber, to realize an optical transmission acrossa broad bandwidth including wavelengths of 658 nanometers to 1556nanometers. As for the holey fiber, some improvements have been made interms of the length of the fiber used and the transmission loss (see,for example, K. Kurokawa, K. Tajima, K. Tsujikawa, K. Nakajima, T.Matsui, I. Sankawa, and T. Haibara, “Penalty-free dispersion-managedsoliton transmission over a 100-km low-loss PCF”, J. Lightwave Technol.,vol. 24, no. 1, pp. 32-37 (2006) and K. Tajima, “Low loss PCF byreduction of hole surface imperfection”, ECOC 2007, PD 2.1 (2007)). Forexample, K. Tajima, “Low loss PCF by reduction of hole surfaceimperfection”, ECOC 2007, PD 2.1 (2007) discloses a holey fiber that canreduce a transmission loss as low as about 0.18 dB/km at a wavelength of1.55 micrometers. As just described, the broadband optical transmissionusing a holey fiber is a technology having a sufficient potential to bepractically used in the future.

Characteristics of a holey fiber are mainly determined by a ratio d/Λ,which is a ratio of a diameter d of a hole to a distance Λ betweenadjacent holes. M. Koshiba and K. Saitoh, “Applicability of classicaloptical fiber theories to holey fibers”, Opt. Lett., vol. 29, no. 15,pp. 1739-1741 (2004) discloses that a holey fiber having holes arrangedin a form of triangular lattice can realize a single-mode transmissionat all wavelengths by setting d/Λ equal to or less than 0.43. Thecharacteristic of being able to realize the single-mode transmission atall wavelengths is called the Endlessly Single-Mode (ESM)characteristic. If the single-mode transmission is realized in thismanner, a faster optical transmission can be achieved. At the same time,a coupling of a light with a higher-order mode of the holey fiber can beprevented when the light is input into the holey fiber connected toanother optical fiber and alike, thus preventing an increase of aconnection loss.

As a type of the holey fiber, a multi-core holey fiber having aplurality of cores arranged separately from each other is disclosed (seeInternational Publication No. WO 2006/100488 Pamphlet). Because themulti-core holey fiber can transmit a different optical signal througheach of the cores, for example, it is considered to enable an ultra-highcapacity transmission by way of a space division multiplexing (SDM)transmission.

However, with the conventional holey fiber, both an ordinary holey fiberhaving a single core and a multi-core holey fiber having a plurality ofcores have a problem that a bending loss sharply increases particularlyat the short-wavelength side as an operation wavelength band increases.

For example, the holey fiber disclosed in K. Ieda, K. Kurokawa, K.Tajima, and K. Nakajima, “Visible to infrared high-speed WDMtransmission over PCF,” IEICE Electron. Express, vol. 4, no. 12, pp.375-379 (2007) shows that a bending loss occurred when the fiber iswound ten times in a radius of 15 millimeters is 0.1 dB at a wavelengthof 658 nanometers. However, when the inventors of the present inventionexperimented using a finite element method (FEM) simulation with theparameters (Λ=7.5 micrometers, d/Λ=0.5) disclosed in K. Ieda, K.Kurokawa, K. Tajima, and K. Nakajima, “Visible to infrared high-speedWDM transmission over PCF,” IEICE Electron. Express, vol. 4, no. 12, pp.375-379 (2007), the bending loss of the fiber wound at a diameter of 20millimeters is as high as 10 dB/m at the wavelength of 658 nanometers,which is considerably high. In addition, if d/Λ is reduced to achievethe ESM characteristic, the bending loss is considered to increasebecause an effective refractive index difference between the core andthe cladding is also reduced.

SUMMARY OF THE INVENTION

It is an object of the present invention to at least partially solve theproblems in the conventional technology.

According to one aspect of the present invention, there is provided anoptical transmission system including an optical transmitting unit thatoutputs at least one optical signal having a wavelength included in anoperation wavelength band and a holey fiber that is connected to theoptical transmitting unit. The holey fiber includes a core through whichthe optical signal is transmitted and a cladding formed around the core.The cladding includes a plurality of holes formed around the core in atriangular lattice shape. The holey fiber transmits the optical signalin a single mode. A bending loss of the holey fiber is equal to or lessthan 5 dB/m at a wavelength in the operation wavelength band when theholey fiber is wound at a diameter of 20 millimeters.

Furthermore, according to another aspect of the present invention, thereis provided an optical transmission system including an opticaltransmitting unit that outputs at least one optical signal having awavelength included in an operation wavelength band; a holey fiber thatis connected to the optical transmitting unit and that includes aplurality of cores separated from each other through each of which theoptical signal is transmitted, and a cladding formed around the cores,the cladding including a plurality of holes arranged around each of thecores in a triangular lattice shape; an optical multiplexing unit thatmultiplexes optical signals output from the optical transmitting unit;an optical demultiplexing unit that demultiplexes the optical signalstransmitted through the holey fiber; and an optical receiving unit thatreceives the optical signals demultiplexed by the optical demultiplexingunit. The holey fiber transmits the optical signal in a single modethrough each of the cores. A bending loss of the holey fiber is equal toor less than 5 dB/m at a wavelength in the operation wavelength bandwhen the holey fiber is wound at a diameter of 20 millimeters.

Moreover, according to still another aspect of the present invention,there is provided a multi-core optical fiber including a plurality ofcores through each of which an optical signal is transmitted and acladding formed around the cores. At least one of the cores is arrangedat a position offset from a standard arrangement position where each ofthe cores is arranged in a rotational symmetry around a center axis ofthe cladding.

Furthermore, according to still another aspect of the present invention,there is provided a multi-core optical fiber including a plurality ofcores through each of which an optical signal is transmitted and acladding formed around the cores. The cores are arranged at standardarrangement position where each of the cores is arranged in a rotationalsymmetry around a center axis of the cladding. At least one of thestandard arrangement positions is excluded from an arrangement of acore.

The above and other objects, features, advantages and technical andindustrial significance of this invention will be better understood byreading the following detailed description of presently preferredembodiments of the invention, when considered in connection with theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an optical transmission system according toa first embodiment of the present invention;

FIG. 2 is a schematic sectional view of an HF shown in FIG. 1;

FIG. 3 is a schematic of wavelength dependency of a bending losscalculated using FEM simulation by changing A from 4 micrometers to 10micrometers while fixing d/Λ to 0.43 in the HF having the structureshown in FIG. 2;

FIG. 4 is a schematic of a relationship between Λ and the minimumwavelength where the bending loss becomes 5 dB/m, or 1 dB/m that is amore preferable value, in FIG. 3;

FIG. 5 is a graph plotting a relationship between the minimum wavelengthand Λ shown in FIG. 4;

FIG. 6 is a schematic of a relationship between Λ and the minimumwavelength where the bending loss becomes 1 dB/m when d/Λ is 0.40, 0.43,0.48, and 0.50, respectively, in an HF having the same structure as oneshown in FIG. 2;

FIG. 7 is a schematic of wavelength dependency of a confinement losscalculated using the FEM simulation by changing Λ from 2 micrometers to10 micrometers while fixing d/Λ to 0.43 in the HF having the structureshown in FIG. 2;

FIG. 8 is a schematic of relationship between Λ and the maximumwavelength where the confinement loss becomes 0.01 dB/km, or 0.001 dB/kmthat is a more preferable value, in FIG. 7;

FIG. 9 is a graph plotting the relationship between the maximumwavelength and Λ, shown in FIG. 8;

FIG. 10 is a schematic of a relationship between Λ and the maximumwavelength where the confinement loss becomes 0.001 dB/km when d/Λ is0.40, 0.43, and 0.48, respectively, in an HF having the same structureas one shown in FIG. 2;

FIG. 11 is a diagram including both of lines indicating the minimumwavelengths where the bending loss become equal to or less than 5 dB/mor 1 dB/m as shown in FIG. 5, and lines indicating the maximumwavelengths where the confinement loss becomes equal to or less than0.01 dB/km or 0.001 dB/km as shown in FIG. 9;

FIG. 12 is a schematic of wavelength dependency of the bending losscalculated using the FEM simulation by changing the number of holelayers from four to five and further to six while fixing d/Λ to 0.43 andΛ to 7 micrometers in the HF having holes arranged in a form oftriangular lattice as shown in FIG. 2;

FIG. 13 is a schematic of a relationship between the number of the holelayers and the minimum wavelength where the bending loss becomes 1 dB/min FIG. 12;

FIG. 14 is a graph plotting the relationship between the minimumwavelength and the number of the hole layers shown in FIG. 13;

FIG. 15 is a schematic of wavelength dependency of the confinement losscalculated using the FEM simulation by changing the number of holelayers from four to five and further to six while fixing d/Λ to 0.43 andΛ to 7 micrometers in the HF having holes arranged in a form oftriangular lattice as shown in FIG. 2;

FIG. 16 is a schematic of a relationship between the number of the holelayers and the maximum wavelength where the confinement loss becomes0.001 dB/km in FIG. 15;

FIG. 17 is a graph plotting the relationship between the maximumwavelength and the number of the hole layers, shown in FIG. 16;

FIG. 18 is a schematic of a relationship between the combination of d/Λand Λ, the minimum wavelength where the bending loss becomes 1 dB/m, andthe effective core area at the wavelength of 1.55 micrometers in the HFhaving the structure shown in FIG. 2;

FIG. 19 is a graph plotting a relationship between the minimumwavelength where the bending loss becomes 1 dB/m and the effective corearea, shown in FIG. 18;

FIG. 20 is a schematic of a relationship between the combination of d/Λand Λ, the maximum wavelength where the confinement loss becomes 0.001dB/km, and the effective core area at the wavelength of 1.55 micrometersin the HF having the structure shown in FIG. 2;

FIG. 21 is a graph plotting the relationship between the maximumwavelength where the confinement loss becomes 0.001 dB/km and theeffective core area, shown in FIG. 20;

FIG. 22 is a schematic of a relationship between Λ and the effectivecore area when the wavelength is at 0.55 micrometers, 1.05 micrometers,and 1.55 micrometers, respectively, and d/Λ is fixed to 0.43, in the HFhaving the structure shown in FIG. 2;

FIG. 23 is a schematic of optical characteristics of an HF with d/Λ=0.43and Λ=5 micrometers at each of the wavelengths;

FIG. 24 is a schematic of the wavelength dependency of the bending lossand the confinement loss in the HF with d/Λ=0.43 and Λ=5 micrometers;

FIG. 25 is a block diagram of an optical transmission system accordingto a second embodiment of the present invention;

FIG. 26 is a schematic sectional view of a multi-core HF shown in FIG.25;

FIG. 27 is a schematic of a field distribution of light having awavelength of 1.55 micrometers and propagating through a core in themulti-core HF;

FIG. 28 is a schematic of a field distribution of light having awavelength of 1.55 micrometers and propagating through a core in themulti-core HF;

FIG. 29 is a schematic of a confinement loss, a wavelength dispersion,an effective core area, and a bending loss at the wavelength of 1.55micrometers in a single-core HF and the multi-core HF;

FIG. 30 is a schematic of wavelength dependency of bending losses in thesingle-core HF and the multi-core HF;

FIG. 31 is a schematic of field distribution of light intensity, shownin contour lines, when the light propagates through a core of themulti-core HF at the wavelength of 1.55 micrometers;

FIG. 32 is a schematic of field distribution of light intensity, shownin contour lines, when the multi-core HF, shown in FIG. 31, is bent;

FIG. 33 is a sectional photograph of the manufactured multi-core HF;

FIG. 34 is a schematic of wavelength dependency of a bending loss whenthe light was propagated through the core of the manufactured multi-coreHF;

FIG. 35 is a schematic of crosstalk measurement results in themanufactured multi-core HF;

FIG. 36 is a schematic of an exemplary bend applying unit included inthe optical transmission system according to the second embodiment;

FIG. 37 is a schematic of an exemplary lateral pressure applying unitincluded in the optical transmission system according to the secondembodiment;

FIG. 38 is a schematic sectional view of a multi-core HF according to athird embodiment of the present invention;

FIG. 39 is a schematic for explaining connection of the multi-core HFsshown in FIG. 26;

FIG. 40 is a schematic for explaining the connection of the multi-coreHFs shown in FIG. 38;

FIG. 41 is a schematic of the right side multi-core HF shown in FIG. 40rotated for 120 degrees;

FIG. 42 is a schematic sectional view of a multi-core HF according to afirst modification;

FIG. 43 is a schematic sectional view of a multi-core HF according to asecond modification;

FIG. 44 is a schematic sectional view of a multi-core HF according to athird modification;

FIG. 45 is a schematic sectional view of a multi-core HF according to afourth modification;

FIG. 46 is a schematic sectional view of a multi-core optical fiberaccording to a fourth embodiment of the present invention; and

FIG. 47 is a schematic sectional view of a multi-core HF according to afifth embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Exemplary embodiments of an optical transmission system and a multi-coreoptical fiber according to the present invention will be explained indetail below with reference to the accompanying drawings. It should beunderstood that these embodiments are not intended to limit the scope ofthe present invention. A bending loss is defined as a loss accrued whenan optical fiber is wound at a diameter of 20 millimeters. The terms notespecially defined herein shall follow the definitions and themeasurement methods defined in the International Telecommunication UnionTelecommunication Standardization Sector (ITU-T) G.650.1.

FIG. 1 is a block diagram of an optical transmission system 10 accordingto a first embodiment of the present invention. As shown in FIG. 1, theoptical transmission system 10 according to the first embodimentincludes an optical transmitting apparatus 1, an HF 2 connected to theoptical transmitting apparatus 1, and an optical receiving apparatus 3connected to the HF 2. The optical transmitting apparatus 1 furtherincludes optical transmitters 11 to 13, each outputting an opticalsignal having a different wavelength from each other, and an opticalmultiplexer 14 that multiplexes each of the signals output from theoptical transmitters 11 to 13 and outputs the multiplexed signal to theHF 2. The optical receiving apparatus 3 includes an opticaldemultiplexer 34 that demultiplexes the optical signal multiplexed andtransmitted over the HF 2 to each of the optical signals, and opticalreceivers 31 to 33 respectively receiving each of the demultiplexedsignals.

The optical signals output from the optical transmitters 11 to 13 are,for example, laser beams modulated with a non-return-to-zero (NRZ)signal whose modulation speed is 10 Gbps. Wavelengths of these opticalsignals are 0.55 micrometers, 1.05 micrometers, and 1.55 micrometers,respectively. These wavelengths are distributed in a broad wavelengthbandwidth having a center thereof at approximately 1 micrometer. The HF2 transmits each of the optical signals in a single mode. A bending losscharacteristic of the HF 2 is equal to or less than 5 dB/m at thewavelength of each of these optical signals included in an operationwavelength band. Therefore, the HF 2 can transmit each of the opticalsignals in the single mode with a bending loss that is practically lowenough. The optical receivers 31 to 33 receive each of the opticalsignals transmitted over the HF 2 and demultiplexed by the opticaldemultiplexer 34. The optical receivers 31 to 33 extract the NRZ signalfrom each of the optical signals as an electrical signal. In thismanner, the optical transmission system 10 can transmit optical signalsin the single mode in a broad bandwidth with a low bending loss.

A specific structure of the HF 2 will now be explained. FIG. 2 is aschematic sectional view of the HF 2 shown in FIG. 1. As shown in FIG.2, the HF 2 includes a core 21 arranged at the center thereof, and acladding 22 arranged on the external circumference of the core 21. Thecladding 22 has a plurality of holes 23 periodically arranged around thecore 21. The core 21 and the cladding 22 are made of silica based glass.The holes 23 are arranged in a form of a triangular lattice La, inlayers of a regular hexagon surrounding the core 21. In the HF 2, thenumber of these hole layers is five.

When a diameter of the hole 23 is denoted as d [μm], and a latticeconstant of a triangular lattice La is denoted as Λ [μm], d/Λ is 0.43.Therefore, the HF 2 achieves the ESM characteristics across the entireoperation wavelength band that is between 0.55 micrometers and 1.55micrometers. Furthermore, in the HF 2, when the minimum wavelength inthe operation wavelength band, that is 0.55 micrometers, is denoted asλ_(s) [μm], Λ is set to 5 micrometers correspondingly to λ_(s) so thatΛ≦−0.518λ_(s) ²+6.3617λ_(s)+1.7468 is established. As a result, in theHF 2, the bending loss becomes equal to or less than 5 dB/m that is abending loss practically low enough, at the wavelengths of each of theoptical signal included in the operation wavelength band.

A specific explanation will be provided below. FIG. 3 is a schematic ofwavelength dependency of the bending loss in the HF having the structureshown in FIG. 2. In this diagram, the wavelength dependency iscalculated using the FEM simulation by changing Λ from 4 micrometers to10 micrometers while fixing d/Λ to 0.43. Lines L1 to L7 are curvesrepresenting the wavelength dependency of the bending loss when Λ is 4micrometers, 5 micrometers, 6 micrometers, 7 micrometers, 8 micrometers,9 micrometers, and 10 micrometers, respectively. As shown in FIG. 3, allof the lines L1 to L7 indicate that the bending loss rises towardshorter end of the wavelengths. At the same time, when Λ becomessmaller, the wavelength, where the bending loss increases, is shiftedtoward the shorter end of the wavelengths. FIG. 4 is a schematic of arelationship between Λ and the minimum wavelength where the bending lossbecomes 5 dB/m, or 1 dB/m that is a more preferable value, in FIG. 3. Inother words, such a bending loss, which is equal to or less than 5 dB/mor 1 dB/m, can be achieved at wavelengths longer than those shown inFIG. 4 for each of the values of Λ. FIG. 5 is a graph plotting therelationship between the minimum wavelength and Λ shown in FIG. 4. LinesL8 and L9 are curves respectively representing such a relationship whenthe bending loss is 5 dB/m or 1 dB/m. Each of these lines is expressedby formulas Λ=−0.518λ_(s) ²+6.3617λ_(s)+1.7468, and Λ=−0.739λ_(s)²+6.3115λ+1.5687.

The line L8 shown in FIG. 5 specifies the minimum wavelength where thebending loss becomes equal to or less than 5 dB/m. Therefore, in themanner according to the first embodiment, if Λ is set for the HF 2correspondingly to λ_(s) that is the minimum wavelength within theoperation wavelength band so that Λ≦−0.518λ_(s) ²+6.3617λ_(s)+1.7468 isestablished, it is possible to make the bending loss equal to or lessthan 5 dB/m at the wavelength of each of the optical signals.

In the HF 2 according to the first embodiment, d/Λ is 0.43; however, thepresent invention is not limited to this value, and the ESMcharacteristic can be realized with a value less than 0.43. FIG. 6 is aschematic of a relationship between Λ and the minimum wavelength wherethe bending loss becomes 1 dB/m when d/Λ is 0.40, 0.43, 0.48, and 0.50in an HF having the same structure as one shown in FIG. 2. Lines L10 toL13 are curves representing the relationship when d/Λ is 0.40, 0.43,0.48, and 0.50, respectively. As shown in FIG. 6, when d/Λ becomessmaller, the minimum wavelength, realizing a bending loss equal to orless than 1 dB/m for the given Λ, becomes longer. Therefore, d/Λ is setaccordingly to a desired operation wavelength band.

A confinement loss in the HF 2 according to the first embodiment willnow be explained. An HF generally has a characteristic called aconfinement loss. This is a loss that occurs due to the light leakingfrom the hole structure. As described above, because the transmissionloss has become reduced approximately to 0.18 dB/km in a conventional HFat the wavelength of 1550 nanometers, it is preferable to make theconfinement loss equal to or less than 0.01 dB/km or 0.001 dB/km that issufficiently low in comparison with the transmission loss.

Because Λ is set to 5 micrometers in the HF 2 according to the firstembodiment, when 1.55 micrometers, the maximum wavelength in theoperation wavelength band, is denoted as λ₁ [μm], Λ≧−0.1452λ₁²+2.982λ₁+0.1174 is established. Therefore, the HF 2 achieves aconfinement loss equal to or less than 0.01 dB/km, that is sufficientlylow, in each of the wavelength of the optical signals.

A specific explanation will now be provided. FIG. 7 is a schematic ofwavelength dependency of the confinement loss. In this diagram, thewavelength dependency is calculated using the FEM simulation by changingΛ from 2 micrometers to 10 micrometers while fixing d/Λ to 0.43. LinesL14 to L22 are curves representing the wavelength dependency of theconfinement loss when Λ is 2 micrometers, 3 micrometers, 4 micrometers,5 micrometers, 6 micrometers, 7 micrometers, 8 micrometers, 9micrometers, and 10 micrometers, respectively. As shown in FIG. 7, allof the lines L14 to L22 indicate that the confinement loss rises towardthe longer end of the wavelengths. At the same time, the greater Λ is,the smaller the confinement loss becomes toward the longer end of thewavelengths. FIG. 8 is a schematic of the relationship between Λ and themaximum wavelength where the confinement loss becomes 0.01 dB/km, or0.001 dB/km that is a more preferable value, in FIG. 7. In other words,it is possible to achieve a confinement loss equal to or less than 0.01dB/km or 0.001 dB/km at a wavelength shorter than that shown in FIG. 8for each of the values of Λ. FIG. 9 is a graph plotting the relationshipbetween the maximum wavelength and Λ shown in FIG. 8. Lines L23 and L24are curves representing the relationships when the confinement loss is0.01 dB/km and 0.001 dB/km, respectively, and each of these lines isexpressed by a formula, Λ=−0.1452λ₁ ²+2.982λ₁+0.1174, and λ=−0.0801λ₁²+3.6195λ₁+0.3288, respectively.

The line L23 shown in FIG. 9 indicates the maximum wavelength where theconfinement loss becomes equal to or less than 0.01 dB/km. In the HF 2according to the first embodiment, because Λ≧−0.1452λ₁ ²+2.982λ₁+0.1174is established for λ₁ that is the maximum wavelength within theoperation wavelength band, the confinement loss becomes equal to or lessthan 0.01 dB/km at each of the wavelengths of the optical signals.

FIG. 10 is a schematic of a relationship between Λ and the maximumwavelength where the confinement loss becomes 0.001 dB/km, when d/Λ is0.40, 0.43, and 0.48, respectively, in an HF having the same structureas one shown in FIG. 2. Lines L25 to L27 are curves representing therelationship when d/Λ is 0.40, 0.43, and 0.48, respectively. As shown inFIG. 10, when d/Λ becomes smaller, the maximum wavelength, realizing aconfinement loss equal to or less than 0.001 dB/km for the given Λ,becomes shorter. Therefore, d/Λ is set accordingly to a desiredoperation wavelength band.

FIG. 11 is a diagram including both of the lines L8 and L9 indicatingthe minimum wavelengths where the bending loss becomes equal to or lessthan 5 dB/m or 1 dB/m as shown in FIG. 5, and the lines L23 and L24indicating the maximum wavelengths where the confinement loss becomesequal to or less than 0.01 dB/km or 0.001 dB/km as shown in FIG. 9. Inthe optical transmission system 10 according to the first embodiment,the operation wavelength band is between 0.55 micrometers and 1.55micrometers, and Λ is 5 micrometers in the HF 2. These conditionscorrespond to an area between the line L8 and the line L23. Therefore,the optical transmission system 10 can transmit each of the opticalsignals having the wavelengths included in the operation wavelength bandwith a low bending loss equal to or less than 5 dB/m, and a lowconfinement loss equal to or less than 0.001 dB/km.

According to the first embodiment, the number of the hole layers arefive in the HF 2; however, the present invention is not limited to sucha number. Hole layer dependency of the bending loss in the HF will nowbe explained. FIG. 12 is a schematic of wavelength dependency of thebending loss in the HF having holes arranged in a form of triangularlattice as shown in FIG. 2. In this diagram, the wavelength dependencyis calculated using the FEM simulation by changing the number of thehole layers from four to five and further to six while fixing d/Λ to0.43 and Λ to 7 micrometers. Lines L28, L4, and L29 are curvesrepresenting the wavelength dependency of the bending loss when thenumber of the hole layers is four, five, or six, respectively. The lineL4 is same as the line L4 shown in FIG. 3. As shown in FIG. 12, all ofthese lines L28, L4, and L29 indicate the bending loss rising toward theshorter end of the wavelengths. At the same time, the greater the numberof the hole layer is, the smaller the bending loss becomes in the longwavelength domain. When the bending loss becomes equal to or higher than1 dB/m, the influence thereof should be taken account for thetransmission characteristics. However, in such a wavelength domain, thenumber of the hole layers does not make much difference.

FIG. 13 is a schematic of a relationship between the number of the holelayers and the minimum wavelength where the bending loss becomes 1 dB/min FIG. 12. In other words, if a wavelength is longer than that shown inFIG. 13 for each number of the hole layers, the bending loss will becomeequal to or less than 1 dB/m. FIG. 14 is a graph plotting therelationship between the minimum wavelength and the number of the holelayers shown in FIG. 13. Lines L30, L9, and L31 are curves representingthe relationships when the number of the hole layers is four, five, andsix, respectively. The line L9 is same as the line L9 shown in FIG. 5.As shown in FIG. 14, the minimum wavelength, where the bending lossbecomes equal to or less than 1 dB/m, is less affected by the number ofthe hole layers. Therefore, as long as Λ is selected to satisfy theformula −≦−0.739λ_(s) ²+6.3115λ_(s)+1.5687 in the same manner as in theHF 2, the bending loss of equal to or less than 1 dB/m can be realizedusing an HF having four or six hole layers, instead of the HF havingfive hole layers such as the HF 2 described above.

The hole layer number dependency of the confinement loss in the HF willnow be explained. FIG. 15 is a schematic of wavelength dependency ofconfinement loss in the HF having the holes arranged in triangularlattice, as shown in FIG. 2. In this diagram, the wavelength dependencyis calculated using the FEM simulation by changing the number of thehole layers from four to five and further to six while fixing d/Λ to0.43 and Λ to 7 micrometers. Lines L32, L19, and L33 are curvesrepresenting the wavelength dependency of the confinement loss when thenumber of the hole layers is four, five, or six, respectively. The lineL19 is same as the line 19 shown in FIG. 7. As shown in FIG. 15, any oneof the lines L32, L19, and L33 indicates confinement loss rising towardlonger end of the wavelengths. At the same time, the greater the numberof the hole layer is, the smaller the confinement loss becomes.

FIG. 16 is a schematic of a relationship between the number of holelayers and the maximum wavelength where the confinement loss becomes0.001 dB/km in FIG. 15. In other words, confinement loss equal to orless than 0.001 dB/km can be achieved at a wavelength shorter than thatshown in FIG. 16 for each number of the hole layers. FIG. 17 is a graphplotting the relationship between the maximum wavelength and the numberof the hole layers, shown in FIG. 16. Lines L34, L24, and L35 are curvesrepresenting the relationships when the number of the hole layers isfour, five or six, respectively, and each of these curves is expressedby a formula Λ=−2.0416λ₁ ²+12.87λ₁+1.7437, Λ=−0.0801λ₁²+3.6195λ₁+0.3288, or Λ=−0.0995λ₁ ²+2.438λ₁+0.337. The line L24 is sameas the line L24 shown in FIG. 9. Therefore, as long as Λ is selected tosatisfy the formula Λ≧−2.0416λ₁ ²+12.87λ₁+1.7437 when the number of thehole layer is four, and the formula Λ≧−0.0995λ₁ ²+2.438λ₁+0.337 when thenumber of the hole layer is six, the confinement loss of equal to orless than 0.001 dB/km can be realized using an HF having four or sixhole layers, instead of the HF having five hole layers such as the HF 2described above.

The number of optical signals used is not limited to three as describedin the first embodiment. The number of optical signals may be any numberof one or more as long as the optical signals is at a wavelengthincluded in the operation wavelength band.

When an HF is used as an optical circuit, the larger an effectivesectional area of the core is, the lower optical nonlinearity becomes.Therefore, when the effective sectional area is larger, it isadvantageous for improving the transmission characteristics. Therelationship between d/Λ and Λ, the parameters of an HF, and theeffective core area will now be explained.

FIG. 18 is a schematic of a relationship between the combination of d/Λand Λ, the minimum wavelength where the bending loss becomes 1 dB/m, andthe effective core area (Aeff) when the wavelength is 1.55 micrometersin the HF having the structure shown in FIG. 2. FIG. 19 is a graphplotting the relationship between the minimum wavelength where thebending loss becomes 1 dB/m, and the effective core area as shown inFIG. 18. Lines L36 to L39 are curves representing the relationships whend/Λ is 0.40, 0.43, 0.48, and 0.50, respectively. As shown in FIG. 19,when these parameters are combined so that the bending loss becomes 1dB/m at the same minimum wavelength, the greater d/Λ is, the larger theeffective core area becomes.

FIG. 20 is a schematic of a relationship between the combination of d/Λand Λ, the maximum wavelength where the confinement loss becomes 0.001dB/km, and the effective core area when the wavelength is 1.55micrometers in the HF having the structure shown in FIG. 2. FIG. 21 is agraph plotting the relationship between the maximum wavelength where theconfinement loss becomes 0.001 dB/km and the effective core area asshown in FIG. 20. Lines L40 to L42 are curves representing therelationships when d/Λ is 0.40, 0.43, and 0.48, respectively. As shownin FIG. 21, when these parameters are combined so that the confinementloss becomes 0.001 dB/km at the same maximum wavelength, the greater d/Λis, the larger the effective core area becomes, in the same manner asshown in FIG. 19. Therefore, upon designing an HF, it is preferable touse a combination of the parameters with d/Λ as high as possible becausethe effective core area increases; however, d/Λ should be kept equal toor less than 0.43 to maintain the ESM characteristic. In the abovedescription, 1 dB/m and 0.001 dB/km are used as standard values of thebending loss and the confinement loss, respectively. However, the sameconclusion can also be led when 5 dB/m and 0.01 dB/km are used as thestandard values of the bending loss and the confinement loss,respectively.

FIG. 22 is a schematic of a relationship between Λ and the effectivecore area when the wavelength is at 0.55 micrometers, 1.05 micrometers,and 1.55 micrometers, respectively, and d/Λ is fixed to 0.43, in the HFhaving the structure shown in FIG. 2. Lines L43 to L45 are curvesrepresenting the relationships when the wavelength is 0.55 micrometers,1.05 micrometers, and 1.55 micrometers, respectively. As shown in FIG.22, the larger Λ is, the greater the effective core area becomes at anyof these wavelengths. Differences in these sectional core areas aresmall among these wavelengths.

FIG. 23 is a schematic of optical characteristics of an HF with d/Λ=0.43and Λ=5 micrometers at each of the wavelengths. In FIG. 23, “Aeff”indicates the effective core area. FIG. 24 is a schematic of thewavelength dependency of the bending loss and the confinement loss inthe HF with d/Λ=0.43 and Λ=5 micrometers. The lines L2 and L17 are sameas those respectively shown in FIG. 3 and FIG. 7. As shown in FIGS. 23and 24, the HF having d/Λ=0.43 and Λ=5 micrometers realizes a lowbending loss equal to or less than 5 dB/m and a low confinement lossequal to or less than 0.01 dB/km at wavelengths between 0.55 and 1.55micrometers. Also, as shown in FIG. 23, it has been confirmed that theeffective core area is little dependent on the wavelength, and thewavelength dispersion is greatly dependent on the wavelength.

FIG. 25 is a block diagram of an optical transmission system 20according to a second embodiment of the present invention. As shown inFIG. 25, the optical transmission system 20 according to the secondembodiment includes an optical transmitting apparatus 4, a multi-core HF5 connected to the optical transmitting apparatus 4, and an opticalreceiving apparatus 6 connected to the multi-core HF 5. The opticaltransmitting apparatus 4 further includes seven optical transmitters 41to 47, each outputting an optical signal having a different wavelengthfrom each other, and an optical multiplexer 48 multiplexing each of thesignals output from the optical transmitters 41 to 47 and outputting themultiplexed signal to the multi-core HF 5. The optical receivingapparatus 6 includes an optical demultiplexer 68 demultiplexing theoptical signal multiplexed and transmitted over the multi-core HF 5 fromthe multi-core HF 5, and optical receivers 61 to 67 respectivelyreceiving each of the demultiplexed signals.

The optical signals output from the optical transmitters 41 to 47 are,for example, laser beams modulated by a NRZ signal whose modulationspeed is 10 Gbps. A wavelength of each of these optical signals is 0.55micrometers, 0.85 micrometers, 0.98 micrometers, 1.05 micrometers, 1.31micrometers, 1.48 micrometers, and 1.55 micrometers, respectively. Thesewavelengths are distributed in a broad wavelength bandwidth having acenter thereof at approximately 1 micrometer.

A specific structure of the multi-core HF 5 will now be explained. FIG.26 is a schematic sectional view of the multi-core HF 5 shown in FIG.25. As shown in FIG. 26, the multi-core HF 5 includes cores 511 to 517arranged separately from each other, and a cladding 52 arranged aroundthe external circumference of the cores 511 to 517. The core 511 isarranged at the approximate center of the cladding 52, and the cores 512to 517 are disposed at the tips of a regular hexagon having the centerthereof at the core 511. The cladding 52 is provided with a plurality ofthe holes 53 arranged at intervals around the cores 511 to 517. Theholes 53 are arranged in a form of triangular lattice Lb in layers ofregular hexagons to surround each of the cores 511 to 517. In themulti-core HF 5, each of the cores 511 to 517 are surrounded by at leastfive layers of the holes, and four holes 53 are disposed between each ofthe cores 511 to 517. The cores 511 to 517 and the cladding 52 are madeof silica based glass.

The optical multiplexer 48 multiplexes the optical signals, each outputfrom each of the optical transmitters 41 to 47, onto each of the cores511 to 517 of the multi-core HF 5. Thus, the optical signals output fromthe optical transmitters 41 to 47 are transmitted over different cores511 to 517. The optical demultiplexer 68 demultiplexes each of theoptical signals transmitted over each of the cores 511 to 517 of themulti-core HF 5 from the multi-core HF 5, and guides each of the opticalsignals to the optical receivers 61 to 67. Each of the optical receivers61 to 67 receives each of the demultiplexed optical signals, andextracts the NRZ signal from each of the demultiplexed optical signalsas an electrical signal.

The optical multiplexer 48 is realized by a multiplexer/demultiplexer ofa waveguide type such as an array waveguide grating (AWG), a fiberspliced type, or a spatial coupling type, for example, having sevenstandard single-mode optical fibers at the optical input end, and asingle multi-core HF with the same structure as the multi-core HF 5 atthe optical output end. A demultiplexer having the same structure as theoptical multiplexer 48 may be used as the optical demultiplexer 68.

When the diameter of the holes 53 is denoted as d [μm], and the latticeconstant of the triangular lattice La is denoted as Λ [μm], d/Λ is 0.43.As a result, in the same manner as the HF 2 according to the firstembodiment, the multi-core HF 5 realizes the ESM characteristics acrossthe entire operation wavelength band that is from 0.55 micrometers to1.55 micrometers. Furthermore, in this multi-core HF 5, when 0.55micrometers, the minimum wavelength in the operation wavelength band, isdenoted as λ_(s) [μm], Λ is set to 5 micrometers correspondingly toλ_(s) so that λ≦−0.518λ_(s) ²+6.3617λ_(s)+1.7468 is established. As aresult, in the multi-core HF 5, a bending loss will be equal to or lessthan 5 dB/m at the wavelengths of each of the optical signals includedin the operation wavelength band, in the same manner as in the HF 2according to the first embodiment. Therefore, the multi-core HF 5 cansingle-mode transmission each of the optical signals with a bending lossthat is practically low enough. As described above, the opticaltransmission system 20 is possible to single-mode transmission opticalsignals across a broad bandwidth with low bending loss, as well as torealize a large capacity transmission over SDM.

Furthermore, Λ in the multi-core HF 5 is not limited to 5 micrometers,in the same manner as the first embodiment. As long as Λ is set in themulti-core HF 5 correspondingly to λ_(s), that is the minimum wavelengthwithin the operation wavelength band, so that Λ≦−0.518λ_(s)²+6.3617λ_(s)+1.7468 is established, it is possible to bring the bendingloss to equal to or less than 5 dB/m at the wavelength of each of theoptical signals.

Furthermore, also for the confinement loss, when 1.55 micrometers, themaximum wavelength in the operation wavelength band, is denoted as λ₁[μm], because Λ is set to 5 micrometers with the multi-core HF 5,Λ≦−0.1452λ₁ ²+2.982λ₁+0.1174 is established. As a result, the multi-coreHF 5 achieves a confinement loss equal to or less than 0.01 dB/km thatis sufficiently low at each of the wavelength of the optical signals, inthe same manner as the HF 2 according to the first embodiment.

Furthermore, Λ in the multi-core HF 5 is not limited to 5 micrometers,in the same manner as the first embodiment. As long as Λ is set in themulti-core HF 5 correspondingly to λ¹, that is the maximum wavelengthwithin the operation wavelength band, so that Λ≧−0.1452λ₁²+2.982λ₁+0.1174 is established, it is possible to bring the confinementloss to equal to or less than 0.01 dB/km at the wavelength of each ofthe optical signals.

Furthermore, when the operation wavelength band is between 0.55micrometers and 1.55 micrometers, and Λ is 5 micrometers in themulti-core HF, this condition corresponds to the area between the lineL8 and the line L23 in FIG. 11. Therefore, such a multi-core HF cantransmit each of the optical signals at the wavelengths included in theoperation wavelength band with a low bending loss equal to or less than5 dB/m, as well as with a low confinement loss equal to or less than0.01 dB/km.

The multi-core HF 5 according to the second embodiment will now beexplained more specifically. In the explanation below, the multi-core HF5 is compared with an HF having the same structure as the HF 2 accordingto the first embodiment (hereinafter, referred to as “single-core HF” asappropriate). For both of the multi-core HF 5 and the single-core HF,the design parameters are set to d/Λ=0.43 and Λ=5 micrometers. The cores512 to 517 have the same symmetrical property including the arrangementof the holes 53 arranged therearound; therefore, only thecharacteristics of the core 511, disposed at the center, and the core513 will be explained below.

FIGS. 27 and 28 are schematics of field distributions of light having awavelength of 1.55 micrometers and propagating thorough the core 511 andthe core 513 in the multi-core HF 5, respectively. In FIGS. 27 and 28,the hatched area in the core indicates the field distribution of thelight. In this area, the peak around the center is set to 1, and thehatched pattern is changed for every 0.1. As shown in FIGS. 27 and 28,the light is confined within the core and propagates through either thecore 511 or the core 513.

FIG. 29 is a schematic of a confinement loss, a wavelength dispersion,an effective core area, and a bending loss at the wavelength of 1.55micrometers in the single-core HF and the multi-core HF 5. In FIG. 29,the “SINGLE-CORE” indicates the characteristics of the single-core HF,and the “MULTI-CORE 511” and the “MULTI-CORE 513” respectively indicatethe characteristics of the core 511 and the core 513 of the multi-coreHF 5 when light propagates therethrough. The bending loss of themulti-core HF 5 indicates the loss that occurs when the multi-core HF 5is bent so that the core 513 would come to the inner circumference, andthe core 516 would come to the outer circumference on the surface wherethe cores 511, 513, and 516 are disposed. As shown in FIG. 29, thewavelength dispersions and the effective sectional areas of the corewere all the same for the multi-core 511, the multi-core 513, and thesingle-core. The confinement loss and the bending loss were slightlysmaller in the multi-core 513 than those in the single-core, and muchsmaller in the multi-core 511. It can be considered that the confinementloss and the bending loss are different in each of these scenariosbecause of the difference in the number of the holes provided aroundeach of the cores. In other words, it can be considered that theconfinement loss and the bending loss are extremely low because thenumber of the holes located around the multi-core 511 is much greaterthan those around the single-core having the five hole layers.

FIG. 30 is a schematic of wavelength dependency of the bending losses inthe single-core HF and the multi-core HF 5. A line L2 indicates aspectral curve in the single-core, and is same as the line L2 shown inFIGS. 3 and 24. Lines L2 a, L2 b, and L2 c are spectral curves in thecores 511, 513, and 516, respectively, in the multi-core HF 5. As shownin FIG. 30, the bending losses are low especially in the lines L2 a andL2 c. This is because the confinement loss has a great influence in anarea where the wavelengths is equal to or less than 1 micrometer wherethe bending loss is low from the beginning. On the contrary, in the areawhere the wavelength is equal to or less than 0.8 micrometers where theconfinement loss is low and the influence of the bending loss becomesdominant, almost the same tendency is seen for all of these lines. Inother words, the bending loss in the multi-core HF 5 has acharacteristic similar to that of the single-core HF, regardless ofwhere the core is located.

As shown in FIGS. 29 and 30, the multi-core HF 5 according to thisembodiment has characteristics equal to or better than those of thesingle-core HF having the same design parameters. Therefore, therelationship between the operation wavelength band and the designparameters in the HF 2, explained in the first embodiment, and theoptical characteristics realized thereby also applies to the multi-coreHF 5. In other words, the bending loss can be made equal to or less than5 dB/m at the wavelength of each of the optical signals, for example, ifΛ is set in the multi-core HF 5 so that Λ≦−0.518λ₃ ²+6.3617λ_(s)+1.7468is established correspondingly to λ_(s) that is the minimum wavelengthincluded in the operation wavelength band. Furthermore, the confinementloss can be brought to equal to or less than 0.01 dB/km at thewavelength of each of the optical signals, by allowing the formulaλ≧−0.1452λ₁ ²+2.982λ₁+0.1174 to be established with respect to λ₁ thatis the maximum wavelength included in the operation wavelength band.

Field distributions of light, when the multi-core HF 5 is bent, will nowbe explained. FIG. 31 is a schematic of a field distribution of lightintensity, shown in contour lines, when the light propagates through thecore 511 of the multi-core HF 5 at the wavelength of 1.55 micrometers.In FIG. 31, the contour lines are provided for each 5 dB from the peakthereof to −50 dB. As shown in FIG. 31, when the light propagatesthrough the core 511, the field intensity of the light in the adjacentcores 512 to 517 is lower than the peak by approximately −20 dB. On thecontrary, FIG. 32 is a schematic of a field distribution of lightintensity, shown in contour lines, when the multi-core HF 5 shown inFIG. 31 is bent. As shown in FIG. 32, when the multi-core HF 5 is bent,the light becomes concentrated at the core 511. Therefore, it wasconfirmed that no excessive loss or interference would occur even whenthe multi-core HF 5 is bent.

Then, a multi-core HF, having three cores, was manufactured using aknown stack-and-draw technique to check the basic characteristics of amulti-core HF. FIG. 33 is a sectional photograph of the manufacturedmulti-core HF. The reference letters X, Y, and Z point to the cores. Thedesign parameters of the holes, in this multi-core HF, is set asd/Λ=0.43, and Λ=5 micrometers. Each of the cores X, Y, and Z issurrounded by at least four layers of holes. With respect to thedistances between the cores X, Y, and Z, the cores X and Y are separatedby three hole layers, and the cores X and Z are separated by four holelayers.

Light was injected from one end of this multi-core HF having a length of2 meters. By propagating the light therethrough to measure the opticalcharacteristics of the core X, the wavelength dispersion of 43.6ps/nm/km and the effective core area of 35.9 square micrometers wereobtained. These results were almost same as calculated values shown inFIG. 29. FIG. 34 is a schematic of wavelength dependency of a bendingloss when the light was propagated through the core X of this multi-coreHF. As shown in FIG. 34, the bending losses were quite good and equal toor less than 2 dB/m across the wavelengths between 0.6 micrometers and1.7 micrometers.

Crosstalk was then measured between the cores of the multi-core HFhaving a length of 2 meters in the manner described below. That is,light was injected from one end of the multi-core HF to cause the lightpropagate through the core X; and an optical output received from thecore X, and optical outputs leaked from the core X to the cores Y and Zwere measured at the other end to calculate the crosstalk based on theratio of these measurements. FIG. 35 is a schematic of the measurementresults of the crosstalk in the manufactured multi-core HF. The “X-Y”indicates the crosstalk between the cores X and Y, and the “X-Z”indicates the crosstalk between the cores X and Z. Light beams of twowavelengths, 0.85 micrometers and 1.55 micrometers, were used for thesemeasurements. These measurements were performed without a great bend ofthe multi-core HF, except for the measurement with the light beam havingthe wavelength 0.85 micrometers. This measurement was made with themulti-core HF wound for one time at a diameter of 20 millimeters. Asshown in FIG. 35, the crosstalk was equal to or less than −20 dB betweenthe cores X-Z, having the distance of four hole layers, at eitherwavelength of 0.85 micrometers or 1.55 micrometers. At the wavelength of0.85 micrometers that is the wavelength of the crosstalk was lower, thecrosstalk was improved when the multi-core HF was bent, in comparisonwith that without being bent, in the same manner as the calculationsindicated in FIGS. 31 and 32.

As described above, the interference can be suppressed between the coresto improve the crosstalk, by applying a bend to the multi-core HF.Therefore, the optical transmission system 20 according to the secondembodiment may further include a bend applying unit that applies a bendto the multi-core HF 5 so that this characteristic can be leveraged.FIG. 36 is a schematic of an exemplary bend applying unit included inthe optical transmission system 20 according to the second embodiment. Abobbin 7, that is the bend applying unit, is made of metal or resin, forexample, and has a diameter of 20 millimeters, for example. Themulti-core HF 5 is wound around the bobbin 7 one or more times. In thismanner, the crosstalk between the cores of the multi-core HF 5 can beimproved, in comparison with that without the bobbin 7.

The crosstalk can also be improved by applying a lateral pressures tothe multi-core HF, in the same manner by applying a bend thereto. FIG.37 is a schematic of an exemplary lateral pressure applying unitincluded in the optical transmission system 20 according to the secondembodiment. Lateral pressure applying members 8, which are the lateralpressure applying unit, include two board-like members 8 a and 8 b madeof metal or resin, for example. These board-like members 8 a and 8 bhold the multi-core HF 5, wound one ore more times at a diameter of 20millimeters, therebetween to apply lateral pressures to the multi-coreHF 5. In this manner, the crosstalk between the cores of the multi-coreHF 5 can be improved, in comparison with that without the lateralpressure applying members 8.

The bobbin 7 or the lateral pressure applying members 8 may be providedin a singularity, or in a plurality separated from each other by apredetermined distance, in one section of the optical circuit, that isbetween an optical transmitting apparatus or an optical relay apparatusand another optical relay apparatus or an optical receiving apparatus.Moreover, the bobbin 7 and the lateral pressure applying members 8 maybe used in combination. Furthermore, for suppressing the interferencebetween the cores, it is also possible to use a slot, used for placingthe multi-core HF 5 in an optical cable and lay down the optical cable,as any one of the bend applying unit or the lateral pressure applyingunit or both. Such a slot is usually designed so that a bend or alateral pressure, applied to the optical fiber, is minimized. However,if the slot is designed intentionally to have a diameter, a diameterthereof, a diameter of a spiral groove, or a pitch of a spiral groovethereof so that a bend or lateral pressures is applied to suppress thatthe interference between the cores of the multi-core HF 5, such a slotcan be used as the bend applying unit or the lateral pressure applyingunit. However, it is preferable that any of the bend applying unit orthe lateral applying unit or both only applies a bend to a degree thatthe bending loss will be approximately equal to or less than 3 dB, forexample. In this manner, the bend does not result in an excessivebending loss within one section of an optical circuit.

The optical transmission system according to the present invention isnot limited to those described in the first and the second embodiments.For example, a desired bending loss can be realized in an operationwavelength band by setting Λ of the HF 2 or the multi-core HF 5appropriately to make the minimum wavelength, included in the operationwavelength band, longer than those shown as the line L8 or L9 in FIG.11. Furthermore, a desired confinement loss can be realized by setting Λof the HF appropriately to make the maximum wavelength, included in theoperation wavelength band, shorter than those shown as the line L23 orL24.

To explain it more specifically with an example, if the operationwavelength band is between 0.55 micrometers and 1.7 micrometers, Λ ofthe HF or the multi-core HF is 5 micrometers, and d/Λ thereof is 0.43,then the bending loss becomes equal to or less than 5 dB/m, theconfinement loss becomes equal to or less than 0.01 dB/km, and thesingle-mode transmission can be achieved. Moreover, if the operationwavelength band is between 1.0 micrometers and 1.7 micrometers, Λ of theHF or the multi-core HF is 7 micrometers, and d/Λ thereof is 0.43, thenthe bending loss becomes equal to or less than 1 dB/m and theconfinement loss becomes equal to or less than 0.001 dB/km at thewavelength of each of the optical signals, while the single-modetransmission is also achieved.

According to the second embodiment, the number of the cores in themulti-core HF 5 was seven, however, the number of the cores is notespecially limited thereto. Furthermore, according to the secondembodiment, the optical signals having different wavelengths aremultiplexed onto the different cores of the multi-core HF 5; however,the optical signals having the same wavelength may also be multiplexed.Moreover, the optical transmitters 41 to 47 may outputwavelength-division-multiplexed-(WDM) light, and the WDM light may bemultiplexed onto each of the cores in the multi-core HF 5. The number ofthe optical signals is not especially limited, e.g., may be between 1and 400, as long as the optical signals are at the wavelengths includedin the operation wavelength band.

As described above, according to the present invention, the presentinvention can advantageously realize an optical transmission system thatcan transmit optical signals across a broad bandwidth in the single modewith a low bending loss.

Assuming that, in the multi-core HF shown in FIG. 33, the cores that arethree-fold rotational symmetric around the center axis of the claddingare in a standard arrangement, only the core X is arranged at a positionoffset from the standard arrangement. As a result, a core of themulti-core HF can be advantageously connected easily upon connecting aspecific core thereof to a specific core of another multi-core HF or toan optical apparatus by way of fusion splicing, connector, or mechanicalsplicing. The multi-core HF having such an offset core will now beexplained specifically under a third embodiment of the presentinvention.

FIG. 38 is a schematic sectional view of a multi-core HF 5 a accordingto the third embodiment. The multi-core HF 5 a is different from themulti-core HF 5 in that a core 512 a, corresponding to the core 512 ofthe multi-core HF 5 shown in FIG. 26, is offset from the position of thecore 512 by the lattice constant Λ toward the side of the core 511. Theother cores 511, and 513 to 517, the cladding 52, the holes 53 have thesame structures as those in the multi-core HF 5.

The cores 511 to 517 in the multi-core HF 5 are arranged in six-foldrotational symmetry around the center axis of the cladding 52; on thecontrary, in the multi-core HF 5 a, when the cores that are six-foldrotational symmetric around the center axis of the cladding 52 areconsidered as in a standard arrangement, only one of the cores, i.e.,the core 512 a, is arranged at a position offset from the standardarrangement.

The connectability of the multi-core HF 5 a will now be explained incontrast to that of the multi-core HF 5. To begin with, it is assumedherein that two of the multi-core HFs 5 are connected to each other.FIG. 39 is a schematic for explaining connection of the multi-core HFs 5shown in FIG. 26. As shown in FIG. 39, it is assumed herein that light Lis injected into the core 512 in the multi-core HF 5 at the left side ofthe drawing; a light receiving unit is connected to the end opposing tothe end to be connected in the multi-core HF 5 at the right side of thedrawing; and these multi-core HFs 5 are connected while monitoring theintensity of the light received at the light receiving unit. In thisscenario, if the position of the core 512 in the multi-core HF 5 at theleft side of the drawing is aligned to the position of any one of thecores 512 to 517 of the multi-core HF 5 at the right side of thedrawing, the light L will be coupled from the core 512 in the left sidemulti-core HF 5 to that one of the cores 512 to 517 of the right sidemulti-core HF5, propagate therethrough to the opposite side, and theintensity of the light received at the light receiving unit becomesincreased. At this time, the cores 511, and 513 to 517, other than thecore 512, of the multi-core HF 5 at the left side of the drawing isaligned to any ones of the cores 511 to 517 in the multi-core HF 5 atthe right side of the drawing. In other words, when two of themulti-core HFs 5 are connected without identifying each one of the cores512 to 517, an index of the alignment will be only the intensity of thereceived light.

On the contrary, upon actually deploying a system using multi-coreoptical fibers or inspecting the multi-core optical fiber itself, thereare situations that the cores 512 to 517 need to be identified.According to the above-described method, every time the right sidemulti-core HF 5 is rotated for 60 degrees, the intensity of the receivedlight becomes increased. Therefore, the cores 512 to 517 cannot beidentified. Hence, the intensity of the received light alone cannot beused as the index of alignment of the cores when the cores 512 to 517need to be identified.

FIG. 40 is a schematic for explaining the connection of the multi-coreHFs 5 a shown in FIG. 38. As shown in FIG. 40, it is assumed herein thatthe light L is injected into the core 512 a in the multi-core HF 5 a atthe left side of the drawing; a light receiving unit is connected to theend opposing to the end to be connected in the multi-core HF 5 a at theright side of the drawing; and these multi-core HFs 5 a are connectedwhile monitoring the intensity of the light received at the lightreceiving unit. It is also assumed herein that the cores 512 a of thesemulti-core HFs 5 a are not aligned to each other. In this situation,because the cores 512 a of the multi-core HFs 5 a are offset from theirstandard positions, the light L output from the core 512 a of the leftside multi-core HF 5 a is not coupled to the core 514 of the right sidemulti-core HF 5 a. As a result, the light L hardly propagates to themulti-core HF 5 a at the right side, resulting in extremely weak or zerolight intensity received at the light receiving unit.

Only when the right side multi-core HF 5 a is rotated for 120 degreesfrom the position shown in FIG. 40, as shown in FIG. 41, so that cores512 a of the two multi-core HFs 5 a become aligned, the light L iscoupled from the core 512 a of the multi-core HF 5 a at the left side tothe core 512 a of the multi-core HF 5 a at the right side, andpropagates to the other end, thus increasing the intensity of the lightreceived at the light receiving unit. The intensity of the receivedlight increases only once, during a 360-degree rotation of the rightside multi-core HF 5. Therefore, the intensity of the received lightalone can be used as the index for the core alignment. In this manner,the multi-core HF 5 a enables a specific core to be easily connected toa specific core of another multi-core HF or an optical apparatus.

The multi-core HF 5 a can also be connected easily according to anotherconnection method. For example, two of the multi-core HFs 5 a arepositioned so that one ends thereof face to each other, and a mirror ora prism is inserted between these one ends of the two multi-core HFs 5a. While observing each of these ends of the two multi-core HFs 5 a,made observable by the mirror or the prism, at least one of the two ofthe multi-core HFs 5 a is rotated around the center axis thereof toalign the cores. At this time, the cores of the two multi-core HFs 5 acan be connected easily by determining the rotated position withreference to the core 512 a.

Furthermore, the above connection methods can be combined. Whileobserving the ends with a mirror, for example, the rotated position ofthe two multi-core HFs 5 a may be rotated to adjust the positionsthereof roughly with reference to the cores 512 a, and then furtherrotated to adjust the positions thereof more precisely using a lightintensity monitor. In this manner, the rough and precise adjustments canbe realized quickly and easily.

FIG. 42 is a schematic sectional view of a multi-core HF 5 b accordingto a first modification of the third embodiment. The multi-core HF 5 bis different from the multi-core HF 5 in that a core 512 b,corresponding to the core 512 of the multi-core HF 5 shown in FIG. 26,is offset from the position of the core 512 by the lattice constant Λtoward the opposite side of the core 511. The other cores 511, and 513to 517, the cladding 52, the holes 53 have the same structures as thosein the multi-core HF 5. In other words, in the multi-core HF 5 b, whenthe cores that are six-fold rotational symmetric around the center axisof the cladding 52 are considered as in a standard arrangement, only oneof the cores, i.e., the core 512 b, is arranged at a position offsetfrom the standard arrangement. The multi-core HF 5 b enables specificcores to be connected easily, in the same manner as the multi-core HF 5a.

FIG. 43 is a schematic sectional view of a multi-core HF 5 c accordingto a second modification of the third embodiment. The multi-core HF 5 cis further formed with a plurality of holes 53 a outside the core 512 bin the multi-core HF 5 b shown in FIG. 42. As a result, the multi-coreHF 5 c has five hole layers around the core 512 b, thus enabling theconfinement loss to be reduced in the core 512 b in comparison with themulti-core HF 5 b.

FIG. 44 is a schematic sectional view of a multi-core HF 5 d accordingto a third modification of the third embodiment. The multi-core HF 5 dis different from the multi-core HF 5 in that cores 512 d and 515 d,corresponding to the cores 512 and 515 of the multi-core HF 5 shown inFIG. 26, are offset from the position of the cores 512 and 515 by thelattice constant Λ toward the opposite side of the core 511 or towardthe core 511. The other cores 511, 513, 514, 516, and 517, the cladding52, the holes 53 have the same structures as those in the multi-core HF5. In other words, in the multi-core HF 5 d, when the cores that aresix-fold rotational symmetric around the center axis of the cladding 52are considered as in a standard arrangement, the two cores 512 d and 515d are arranged at positions offset from the standard arrangement. Themulti-core HF 5 d also enables specific cores to be connected easily, inthe same manner as the multi-core HF 5 a.

FIG. 45 is a schematic sectional view of a multi-core HF 5 e accordingto a fourth modification of the third embodiment. The multi-core HF 5 eis different from the multi-core HF 5 in that cores 512 e and 517 e,corresponding to the cores 512 and 517 of the multi-core HF 5 shown inFIG. 26, are offset from the position of the cores 512 and 517 by thelattice constant Λ toward the core 511 or toward the opposite side ofthe core 511. The other cores 511, and 513 to 516, the cladding 52, theholes 53 have the same structures as those in the multi-core HF 5. Inother words, in the multi-core HF 5 e, when the cores that are six-foldrotational symmetric around the center axis of the cladding 52 areconsidered as in a standard arrangement, the two cores 512 e and 517 eare arranged at positions offset from the standard arrangement, and thecores are arranged so as not to have a line-symmetric axis on the crosssection of the multi-core HF 5 e. As a result, in the multi-core HF 5 e,each end of the multi-core HF 5 e (see the ends A and B in FIG. 41) canbe identified.

In other words, when the multi-core HF 5 e is cut, one of the crosssection will be as shown in FIG. 45; and the cross section opposingthereto will be mirror symmetry of the cross section shown in FIG. 45.Because in the multi-core HF 5 e, the two cores 512 e and 517 e arearranged at positions offset from the standard arrangement, and thecores are arranged so as not to have a line-symmetric axis, a specificcore can be identified even on the mirror-symmetrical cross section.Therefore, the multi-core HF 5 e enables the positions of the cores 512e and 517 e to be identified more reliably, as well as those of theother cores, thus enabling the cores to be connected more easily.

FIG. 46 is a schematic sectional view of a multi-core optical fiber 9according to a fourth embodiment of the present invention. As shown inFIG. 46, the multi-core optical fiber 9 is a solid multi-core opticalfiber having no hole. The multi-core optical fiber 9 includes cores 911to 917 arranged separately from each other, and a cladding 92 arrangedaround the external circumference of the cores 911 to 917. The core 911is arranged at the approximate center of the cladding 92. When the coresthat are arranged in a regular hexagon, shown as H, around the centeraxis of cladding 92 are considered as in a standard arrangement, thecores 913 to 917 are disposed at their standard positions, and one ofthe cores, i.e., the core 912, is arranged at a position offset from thestandard arrangement. There is no special limitation as to how far thecores 911 to 917 are separated from each other, or in a diameter of thecores of the cores 911 to 917; the distance is approximately 60micrometers, for example, and the core diameter is approximately 5.0micrometers to 10.0 micrometers. Each of the cores 911 to 917 is made ofsilica based glass added germanium, and the cladding is made of puresilica glass. As a result, the cladding 92 has low refractive index incomparison to that of each of the cores 911 to 917, and relativerefractive index difference of the cores 911 to 917 with respect to thecladding 92 is approximately 0.3 percent to 1.5 percent. The multi-coreoptical fiber 9 confines the light in the each of the cores 911 to 917by way of the refractive index difference, and propagates the lighttherethrough.

Also in the multi-core optical fiber 9, one of the cores, i.e., the core912, is arranged at a position offset from the standard arrangement.Therefore, connection can be easily made in the same manner as themulti-core HF 5 a.

In this manner, the multi-core optical fiber according to the presentinvention may also be a solid multi-core optical fiber.

FIG. 47 is a schematic sectional view of a multi-core HF 5 f accordingto a fifth embodiment of the present invention. The multi-core HF 5 f isdifferent from the multi-core HF 5 in that the multi-core HF 5 f has nocore corresponding to the core 512 in the multi-core HF 5 shown in FIG.26, and an hole 53 f is formed at the position corresponding to the core512. The other cores 511, and 513 to 517, the cladding 52, the holes 53have the same structures as those in the multi-core HF 5. In otherwords, in the multi-core HF 5 f, when the cores that are six-foldrotational symmetric around the center axis of the cladding 52 areconsidered as in a standard arrangement, the cores 513 to 517 arearranged in the standard arrangement except for one position.

The multi-core HF 5 f can be also connected easily in the same manner asthe multi-core HF 5 a. It is assumed herein that light is injected intothe cores 513 to 517 in one of the two multi-core HFs 5 f, uponconnecting the other multi-core HF thereto according to the methodsshown in FIGS. 39 to 41, for example. In this scenario, only when thecores 513 to 517 of the two multi-core HFs 5 f are aligned to eachother, the light is coupled from the cores 513 to 517 of the onemulti-core HF 5 f to the corresponding cores 513 to 517 of the othermulti-core HF 5 f, and propagates to the opposite end, thus increasingthe intensity of the light received at the light receiving unit to themaximum. The intensity of the received light reaches to the maximum onlyonce when the other multi-core HF 5 f is rotated for 360 degrees.Therefore, also in the multi-core HF 5 f, the intensity of the receivedlight alone can be used as an index for aligning the cores, facilitatingeasy connection thereof.

In this manner, the present invention may include a multi-core opticalfiber having cores arranged at the standard arrangement except for oneposition.

As a modification of the multi-core HF 5 f according to the fifthembodiment, the cores may be arranged in the standard arrangement exceptfor two positions, or arranged so as not to have a line-symmetric axis.

Furthermore, according the present invention, the cores may be arrangedin the standard arrangement except for one position, or arranged so asnot to have a line-symmetric axis, also in a solid multi-core opticalfiber such as one according to the fourth embodiment.

The third to fifth embodiments and the modifications thereof aredescribed as examples only; therefore, the cores, the holes forconfining light in the cores, the number thereof, and the arrangementthereof are not limited to those described above. For example, a corearrangement of two- to twelve-fold rotational symmetries may be alsoused as a standard arrangement. Furthermore, it is possible to select,as appropriate, which core should be offset from its standard position,or which standard position should be the one without allocation of thecore.

As described above, according to one aspect of the present invention, itis possible to provide an optical transmission system that enablessingle-mode and large capacity transmission of optical signals in abroad bandwidth with low bending loss, and to provide a multi-coreoptical fiber that can be used in such an optical transmission system,advantageously.

Although the invention has been described with respect to specificembodiments for a complete and clear disclosure, the appended claims arenot to be thus limited but are to be construed as embodying allmodifications and alternative constructions that may occur to oneskilled in the art that fairly fall within the basic teaching herein setforth.

1. An optical transmission system comprising: an optical transmittingunit that outputs at least one optical signal having a wavelengthincluded in an operation wavelength band; an optical fiber that isconnected to the optical transmitting unit, the optical fiber includinga plurality of cores separated from each other through each of which theoptical signal is transmitted, and a cladding formed around the cores;an applying unit that intentionally applies any one of a bend or alateral pressure or both to the optical fiber to suppress interferencesbetween the cores; an optical multiplexing unit that multiplexes opticalsignals output from the optical transmitting unit for inputting theoptical signals to the cores of the optical fiber; an opticaldemultiplexing unit that demultiplexes the optical signals transmittedthrough the optical fiber; and an optical receiving unit that receivesthe optical signals demultiplexed by the optical demultiplexing unit. 2.The optical transmission system according to claim 1, wherein theoptical fiber transmits the optical signal in a single mode through eachof the cores, and a bending loss of the optical fiber is equal to orless than 5 dB/m at a wavelength in the operation wavelength band whenthe optical fiber is wound at a diameter of 20 millimeters.
 3. Theoptical transmission system according to claim 1, wherein the opticalfiber is a holey fiber, the cladding of the holey fiber including aplurality of holes arranged around each of the cores in a triangularlattice shape.
 4. The optical transmission system according to claim 3,wherein the holey fiber has the cores arranged so that four or more ofthe holes are disposed between any two of these cores.
 5. The opticaltransmission system according to claim 3, wherein the operationwavelength band is selected from 0.4 micrometers to 1.7 micrometers,design parameters of the holey fiber satisfy 0.40≦d/Λ≦0.43, andΛ≦−0.518λ_(s) ²+6.3617λ_(s)+1.7468 where Λ is lattice constant of thetriangular lattice in micrometers, d is diameter of each of the holes inmicrometers, and λ_(s) is a minimum wavelength in the operationwavelength band in micrometers.
 6. The optical transmission systemaccording to claim 6, wherein the design parameters of the holey fibersatisfyΛ≦−0.739λ_(s) ²+6.3115λ_(s)+1.5687.
 7. The optical transmission systemaccording to claim 3, wherein design parameters of the holey fibersatisfyΛ≧−0.1452λ₁ ²+2.982λ₁+0.1174 where λ₁ is a maximum wavelength in theoperation wavelength band in micrometers, each of the cores issurrounded by five layers of the holes, and a confinement loss of theholey fiber is equal to or less than 0.01 dB/km at the wavelength in theoperation wavelength band.
 8. The optical transmission system accordingto claim 7, wherein the design parameters of the holey fiber satisfyΛ≧−0.801λ₁ ²+3.6195λ₁+0.3288.
 9. The optical transmission systemaccording to claim 3, wherein design parameters of the holey fibersatisfyΛ≧−0.0995λ₁ ²+2.438λ₁+0.337 where λ₁ is a maximum wavelength in theoperation wavelength band in micrometers, each of the cores issurrounded by six layers of the holes, and a confinement loss of theholey fiber is equal to or less than 0.01 dB/km at the wavelength in theoperation wavelength band.
 10. The optical transmission system accordingto claim 7, wherein the operation wavelength band is selected from 0.55micrometers to 1.7 micrometers, and design parameters of the holey fiberincludes Λ is not less than 5 micrometers.
 11. The optical transmissionsystem according to claim 7, wherein the operation wavelength band isselected from 1.0 micrometers to 1.7 micrometers, design parameters ofthe holey fiber includes Λ is not less than 7 micrometers, a bendingloss of the holey fiber is equal to or less than 1 dB/m when the holeyfiber is wound at a diameter of 20 millimeters at the wavelength in theoperation wavelength band, and a confinement loss of the holey fiber isequal to or less than 0.001 dB/km at the wavelength in the operationwavelength band.
 12. A multi-core optical fiber comprising: a pluralityof cores through each of which an optical signal is transmitted; and acladding formed around the cores, wherein the cores are arranged atstandard arrangement positions where the standard arrangement positionsare arranged in a rotational symmetry around a center axis of thecladding, and at least one of the standard arrangement positions isexcluded from an arrangement of a core.
 13. The multi-core optical fiberaccording to claim 12, wherein the cores are arranged not to have aline-symmetric axis on a cross section of the multi-core optical fiber.